Solve for $x$ and $y$ using elimination. ${-x+4y = 10}$ ${x-3y = -6}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {-x+4y = 10}\thinspace$ to find $x$ ${-x + 4}{(4)}{= 10}$ $-x+16 = 10$ $-x+16{-16} = 10{-16}$ $-x = -6$ $\dfrac{-x}{{-1}} = \dfrac{-6}{{-1}}$ ${x = 6}$ You can also plug ${y = 4}$ into $\thinspace {x-3y = -6}\thinspace$ and get the same answer for $x$ : ${x - 3}{(4)}{= -6}$ ${x = 6}$